asymptotic expectation (english) - meaning, definition, translation, pronunciation

Part of Speech

• Noun Phrase

Phonetic Transcription

• /ˌæ.sɪmˈtɒt.ɪk ˌɛk.spɛkˈteɪ.ʃən/

Meaning and Usage

Meaning: "Asymptotic expectation" refers to the expected value of a random variable as a parameter approaches some limit, typically infinity. This concept is frequently used in statistics and probability theory to analyze the limiting behavior of estimators or random processes.

Usage in English: The term is commonly used in academic writing, particularly in mathematics, statistics, and computer science. It is less frequently used in everyday conversation due to its specialized nature.

Frequency of Use: The term is mainly present in written context, particularly in academic papers, textbooks, and lectures dealing with probability and statistical theory.

Example Sentences: 1. The asymptotic expectation of the algorithm's running time indicates how it will perform on very large inputs. - (La expectativa asintótica del tiempo de ejecución del algoritmo indica cómo funcionará con entradas muy grandes.)

1. In our study, we derived the asymptotic expectation of the estimator to evaluate its efficiency.

2. (En nuestro estudio, derivamos la expectativa asintótica del estimador para evaluar su eficiencia.)

3. Understanding the asymptotic expectation can greatly enhance our predictive models in statistics.

4. (Entender la expectativa asintótica puede mejorar mucho nuestros modelos predictivos en estadística.)

Idiomatic Expressions

While "asymptotic expectation" does not frequently appear in idiomatic expressions in English due to its technical nature, there are several related mathematical and statistical phrases that share a similar context. Here are some examples:

1. Asymptotic behavior: The asymptotic behavior of a function often dictates its long-term performance.

2. (El comportamiento asintótico de una función a menudo dicta su rendimiento a largo plazo.)

3. In the limit: In the limit, the asymptotic expectation of the distribution converges to a normal distribution.

4. (En el límite, la expectativa asintótica de la distribución converge a una distribución normal.)

5. Convergence in distribution: The convergence in distribution leads us to an understanding of the asymptotic expectation.

6. (La convergencia en distribución nos lleva a entender la expectativa asintótica.)

Etymology

• The word "asymptotic" originates from the Greek word "asumptōtos", meaning "not falling together". The term "expectation" comes from the Latin "exspectatio", from "exspectare", meaning "to look out for". In mathematical contexts, these terms combine to describe the expected behavior of a process as it approaches a certain limit.

Synonyms and Antonyms

Synonyms: - Asymptotic mean, expected value of limit.

Antonyms: - Finite expectation, bounded expectation.

This information provides a comprehensive overview of the term "asymptotic expectation", highlighting its meaning, usage, and relevant expressions within its context.